The lifespans of porcupines in a particular zoo are normally distributed. The average porcupine lives $23$ years; the standard deviation is $5.6$ years. Use the empirical rule (68-95-99.7%) to estimate the probability of a porcupine living between $11.8$ and $34.2$ years.
Answer: $23$ $17.4$ $28.6$ $11.8$ $34.2$ $6.2$ $39.8$ $95\%$ We know the lifespans are normally distributed with an average lifespan of $23$ years. We know the standard deviation is $5.6$ years, so one standard deviation below the mean is $17.4$ years and one standard deviation above the mean is $28.6$ years. Two standard deviations below the mean is $11.8$ years and two standard deviations above the mean is $34.2$ years. Three standard deviations below the mean is $6.2$ years and three standard deviations above the mean is $39.8$ years. We are interested in the probability of a porcupine living between $11.8$ and $34.2$ years. The empirical rule (or the 68-95-99.7 rule) tells us that $95\%$ of the porcupines will have lifespans within 2 standard deviations of the average lifespan. The probability of a particular porcupine living between $11.8$ and $34.2$ years is ${95\%}$.